An N=1 3d-3d correspondence
Abstract
M5-branes on an associative three-cycle M 3 in a G 2-holonomy manifold give rise to a 3d N=1 supersymmetric gauge theory, {T}_{N=1}[{M}_3] . We propose an N=1 3d-3d correspondence, based on two observables of these theories: the Witten index and the S 3-partition function. The Witten index of a 3d N=1 theory {T}_{N=1}[{M}_3] is shown to be computed in terms of the partition function of a topological field theory, a super-BF-model coupled to a spinorial hypermultiplet (BFH), on M 3. The BFH-model localizes on solutions to a generalized set of 3d Seiberg-Witten equations on M 3. Evidence to support this correspondence is provided in the abelian case, as well as in terms of a direct derivation of the topological field theory by twisted dimensional reduction of the 6d (2 , 0) theory. We also consider a correspondence for the S 3-partition function of the {T}_{N=1}[{M}_3] theories, by determining the dimensional reduction of the M5-brane theory on S 3. The resulting topological theory is Chern-Simons-Dirac theory, for a gauge field and a twisted harmonic spinor on M 3, whose equations of motion are the generalized 3d Seiberg-Witten equations. For generic G 2-manifolds the theory reduces to real Chern-Simons theory, in which case we conjecture that the S 3-partition function of {T}_{N=1}[{M}_3] is given by the Witten-Reshetikhin-Turaev invariant of M 3.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- July 2018
- DOI:
- 10.1007/JHEP07(2018)052
- arXiv:
- arXiv:1804.02368
- Bibcode:
- 2018JHEP...07..052E
- Keywords:
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- Duality in Gauge Field Theories;
- Field Theories in Higher Dimensions;
- Supersymmetric Gauge Theory;
- Topological Field Theories;
- High Energy Physics - Theory
- E-Print:
- 63 pages, 4 figures